Grandma baked 96 cookies and gave them to her grandchildren. one of the grandchildren, cindy, received 5 fewer cookies than she would have received had all of the cookies been evenly divided among the h grandchildren.
how many cookies did cindy receive?
write your answer as an expression.

If the cookies had been divided equally between the h grandchildren then each grandchild would receive 96/h  cookies.
So Cindy  received (96/h) - 5   cookies

Does not say how many grandchildren. Say n, integer. So, all received some cookies, x, except Cindy, who received 5 less than the even number:

even number= 96/n, Cindy gets 96/n-5, the rest receive the rest of the cookies:

96 - (96/n-5) = 96*(1-1/n) + 5 = 96*(n-1)/n + 5.

Then each of them (n-1) receive the previous number divided by (n-1) -Cindy is not there:

each of the other grandchildren receives:

96/n + 5/(n-1), and Cindy receives 96/n-5, it just needs to be positive.

So any number 'n' which divides 96 and 'n-1' divides 5 works.

Indeed ONLY n=6, makes 5/(6-1) possible.

So there are 6 grandchildren:

5 receive 17 cookies, and Cindy gets 11.

If it were evenly distributed, all would have got 96/6 = 16 cookies.

Now 5 get one more cookie, and Cindy 5 less.

WOW. Very nice problem!! Gonna share it :)

the law of definite proportions states samples of a compound will always contain the same proportion of elements by mass. in other words, a given compound will always contain the same elements in the same proportions by mass.the law of multiple proportions states when two elements combine with each other to form more than one compound, then the weights of one element that combine with a fixed weight of the other are in a ratio of small whole numbers.